JuliaEarth
Implement method of moments
Maximum likelihood fits aren't very robust with GEV distributions. It would be nice to implement the method of moments as an alternative.
Are there similar problems with the GP distribution, or is that part more robust?
Hi @davidanthoff,
I'd have to investigate the theory more carefully to answer it properly. Are you having issues with the GP estimation as well?
No, I'm just starting to play with this, and was wondering whether there was a known problem or not :)
Also, there is https://github.com/jojal5/Extremes.jl, which seems to have MM and some bayesian estimator already? Are there any efforts to merge the two packages? They really seem to do the same thing, right?
Thank you for sharing the package. Will ask if the author is interested in joining efforts here.
I did try the fit for the GP in both packages, got exactly the same results, so I guess that is a good sign :)
That is promising at least :)
I hope to get back to extreme value theory at some point. Currently, my research is too focused on GeoStats.jl, and that is demanding a great amount of :hourglass:
In this library, I have implemented method of moments and probability weighted moments as ways to fit a GPD to data produced using the Peak over Threshold approach:
https://github.com/JuliaDynamics/FractalDimensions.jl/blob/main/src/extremes_based/gpd.jl#L33-L47
The implementations come from the paper: Chaos 33, 073143 (2023) https://doi.org/10.1063/5.0152370
You are interested in section V.A. of the paper, starting at page 6. It shows efficacy of estimators from data sampled directly from a GPD. It shows that maximum likelyhood methods are surprisingly not very good. However the method you have here probably has nothing to do with the method the authors use as "maximum likelyhood".
(p.s. i'll probably add a method using your package in our FractalDimensions.jl package)
It would be awesome to add the method of moments here as well @Datseris so that it reaches a broader audience ❤️